Chieko's mother is following the tour of Hanyu Yuzuru a figure skater.

The Ama~s refer to Inari as a kitsune/fox. While kitsune can be used to describe someone as a "trickster", it's more likely they're commenting on how foxes in Asian folklore are depicted as having the ability to transform into human women who then seduce men.

Of course, Inari's name probably comes from Inari Ookami, a famous fox deity.